Symmetry detection and morphological classification of anatomical structures play pivotal roles in medical image analysis. The application of kinematic surface fitting, a method for characterizing shapes through parametric stationary velocity fields, has shown promising results in computer vision and computer-aided design. However, existing research has predominantly focused on first order rotational velocity fields, which may not adequately capture the intricate curved and twisted nature of anatomical structures. To address this limitation, we propose an innovative approach utilizing a second order velocity field for kinematic surface fitting. This advancement accommodates higher rotational shape complexity and improves the accuracy of symmetry detection in anatomical structures. We introduce a robust fitting technique and validate its performance through testing on synthetic shapes and real anatomical structures. Our method not only enables the detection of curved rotational symmetries (core lines) but also facilitates morphological classification by deriving intrinsic shape parameters related to curvature and torsion. We illustrate the usefulness of our technique by categorizing the shape of human cochleae in terms of the intrinsic velocity field parameters. The results showcase the potential of our method as a valuable tool for medical image analysis, contributing to the assessment of complex anatomical shapes.

翻译：对称性检测与解剖结构的形态分类在医学图像分析中具有关键作用。运动学曲面拟合作为一种通过参数化稳态速度场表征形状的方法，已在计算机视觉与计算机辅助设计领域展现出显著潜力。然而，现有研究主要聚焦于一阶旋转速度场，难以充分捕捉解剖结构复杂的弯曲与扭转特性。针对这一局限，我们提出创新性方法，采用二阶速度场进行运动学曲面拟合。该改进能适应更复杂的旋转形状特征，提升解剖结构对称性检测的精度。我们开发了稳健的拟合技术，并通过合成形状与真实解剖结构的测试验证其性能。该方法不仅能检测弯曲旋转对称性（核心轴线），还可通过推导与曲率及挠率相关的内禀形状参数实现形态分类。我们通过内禀速度场参数对人类耳蜗形状进行分类，验证了该技术的实用性。结果表明，本方法可作为医学图像分析中评估复杂解剖形态的有效工具。